Problem: Determine the value of the following complex number power. Your answer will be plotted in orange. $ ({ e^{\pi i / 4}}) ^ {15} $
Answer: Since $(a ^ b) ^ c = a ^ {b \cdot c}$ $ ({ e^{\pi i / 4}}) ^ {15} = e ^ {15 \cdot (\pi i / 4)} $ The angle of the result is $15 \cdot \frac{1}{4}\pi$ , which is $\frac{15}{4}\pi$ Our result is $ e^{7\pi i / 4}$.